The effectiveness of predictive design and optimization of cell phone networks depends on the accuracy of predicted radio signal strength over the geographic area where service is to be provided. The prediction is made with a mathematical model called a propagation model. Propagation models typically predict radio signal strength given the transmitting antenna pattern and digital terrain maps and clutter maps, although they may also use additional descriptions of the physical environment such as vector data and building databases. Propagation models have a number of parameters whose values are determined by calibrating the model with measurement data. Once a model is calibrated for a particular geographic area, the required signal strength and interference predictions can be carried out.
Model calibration is required to give specific loss characteristics to the physical environment description. For example, the average properties of clutter categories may vary between markets or be unknown altogether. Model calibration assigns optimal values to each clutter category.
The signal strength measurement data used for model calibration is usually either Continuous Wave (CW) data or scanner data. To collect CW data, a clear frequency is selected and a continuous signal is transmitted at that frequency. Data is collected over a drive route. A receiver set to the transmitting frequency collects the data in conjunction with position information from a GPS receiver.
Scanner data is also collected on a drive with simultaneous collection of GPS data. Scanner data is distinct from CW data in that the actual pilot signals from the network are detected, rather than the separate monotone signal used for CW. Signals can be collected from many sites simultaneously, depending on the scanner configuration.
Model calibration is conventionally carried out by finding the parameter set that gives the minimum least-squares (or OLS, for Ordinary Least Squares) fit to the measurement data. Under certain simple assumptions (i.e. that the errors in the data are normally distributed, and that data is an unbiased sample of the underlying population), the OLS fit is the best prediction that can be made.
All measurement data has a finite dynamic range. This generally introduces bias into the measurement data set. Models created by OLS fit to the data may therefore be biased and will not give the best prediction possible.
The effects of the bias due to finite dynamic range are shown in FIGS. 1 and 2. In FIG. 1, received signal strength is shown as a function of distance, along with a simple linear OLS fit to the data. In FIG. 2, the same data set is shown, this time with signals below −100 dBm excluded. The resulting OLS fit predicts less attenuation with distance than does the fit to the full data set shown in FIG. 1. While the OLS fit in FIG. 2 fully reflects the bias in the measurement data set, the Maximum Likelihood (ML) fit (described below) corrects for this bias and gives results nearly equal to those obtained with the full data set.
The example data in FIGS. 1 and 2 is artificial in that the truncation level was applied to the data set, rather than being an inherent feature of it. In real applications, the truncation level or levels are inherent in the data and must be explicitly included in a ML model, as described below. Additionally, a propagation model is usually more complicated than the simple linear fits shown in FIGS. 1 and 2, and will incorporate diffraction and clutter effects among others, as well as antenna discrimination where appropriate. But the figures serve to illustrate the basic issue of bias introduced by limited dynamic range.